Here we start exploring a core of Quantum Computing: Quantum Algorithms. Before we dive into the dark and deep pool of such algorithms, it’s helpful to get familiar with a fundamental constraint to Quantum Computing. In contrast, I’ll also introduce you how powerful qubits get in solving problems through a basic protocol: Quantum Teleportation, the “Hello, world!” of Quantum Programming. No-cloning theorem In terms of computer architechture, it’s convenient to copy the state of a bit in order to create a new qubit exactly the same. ...

Throughout previous posts, I’ve delivered a way to understand what is a quantum measurement. That way of understanding is simple and may suit our normal intuition, but measurement is a non-trivial physical process and somewhat counter-intuitive for several reasons. First, a measurement in general results in probabilistic outcomes. No matter how careful you prepare for the measurement procedure, it is inherent that possible outcomes of a measure is distributed according to a certain probability distribution determined by the state space of your quantum system. ...

Source of image: Quantum Computer Explained - Limits of Human Technology (Kurzgesagt – In a Nutshell) In classical computation, there are four basic operations that act on information bits, namely Identity (no operation), Negation (NOT), Conjunction (AND), and Disjunction (OR). All other operations are secondary and built upon these four operations. That being said, with the primary and secondary operations, one is able to perform any calculation in classical fashion. ...

Quantum entanglement Have you ever thought of a situation when the happening of an event in an isolated environment dictates the result of another event also in an isolated environment with no communication allowed? That sounds infeasible in our view of reality, except that these two separated events share a somewhat telepathic power. Yes, this telepathy really happens in the realm of quantum entanglement. The phenomenon can be simplified that the result of the first measurement reveals information about the result of the second measurement despite an absolute separation and no communication setting. ...

Quantum entanglement is, by definition, a phenomenon that the combined state of a set of qubits cannot be described as a product of the states of each qubit of that set, which also means the entangled state contains hidden information that one cannot reveal through examining separate qubits. In this text, I’m going to introduce and discuss several aspects of this spectacular phenomenon. Measurement in different bases In previous posts, I’ve mentioned that a qubit can be in a superposition of its basis states $\left|0\right\rangle$ and $\left|1\right\rangle$ with corresponding complex amplitudes $a_0$ and $a_1$. ...

Source of image: Quantum Computer Explained - Limits of Human Technology (Kurzgesagt – In a Nutshell) As I’ve mentioned in my previous post, qubits doesn’t suffer from the limitation of only being $0$ or $1$. Within this article, I’m going to talk about some background knowledge essential for ones who have just stepped into the field like me. Single Qubit Dirac notation $\left | \cdot \right\rangle$ (pronounced as ket) is adopted to indicate qubit states. ...